Strange Objects in the Complex Plane
Title | Strange Objects in the Complex Plane |
Publication Type | Journal Article |
Year of Publication | 1983 |
Authors | Widom, M., Bensimon D., Kadanoff L. P., & Shenker S. J. |
Published in | Journal of Statistical Physics |
Issue | 3 |
Page(s) | 443-454 |
Other Numbers | 3493 |
Abstract | Julia sets are examined as examples of strange objects which arise in the study of long time properties of simple dynamical systems. Technically they are the closure of the set of unstable cycles of analytic maps. Physically, they are sets of points which lead to chaotic behavior. The mapf(z)=z2+p is analyzed for smallp where the Julia set is a closed curve, and for largep where the Julia set is completely disconnected. In both cases the Hausdorff dimension is calculated in perturbation theory and numerically. An expression for the rate at which points escape from the neighborhood of the Julia set is derived and tested in a numerical simulation of the escape. |
Bibliographic Notes | Journal of Statistical Physics, Volume 32, No. 3, pp. 443-454 |
Abbreviated Authors | M. Widom, D. Bensimon, L. P. Kadanoff, and S. Shenker |
ICSI Research Group | Networking and Security |
ICSI Publication Type | Article in journal or magazine |